深圳外国语学校高一新生入学摸底试卷

2023-2024学年广东省深圳市高一下学期开学摸底考试英语试题第一部分听力（共两节，满分15分）第一节（共4小题；每小题1分，满分4分）听下面4段对话。

每段对话后有一个小题，从题中所给的A、B、C三个选项中选出最佳选项。

听完每段对话后，你都有10秒钟的时间来回答有关小题和阅读下一个小题。

每段对话仅读一遍。

1. What will the man do on Friday morning?A. Give a lecture.B. Go on a business trip.C. Attend a parents’ meeting.2. What caused the woman to come home late?A. Attending an interview.B. Seeing a doctor.C. Visiting Peter.3. Where will the speakers go?A. To the woman’s house.B. To the man’s company.C. To a restaurant.4. What are the speakers talking about?A. William’s travel experiences.B. The woman’s views on travelling.C. The importance of making travel plans.第二节（共11小题；每小题1分，满分11分）听下面5段对话或独白。

每段对话或独白后有几个小题，从所听到的内容中获取信息，回答相应小题。

听每段对话或独白前，你将有时间阅读各个小题，每小题5秒钟；听完后，各小题将给出5秒钟的作答时间。

每段对话或独白读两遍。

听第5段材料，回答第5、6题。

5. When did Jack begin reading?A. At 4:40.B. At 5:00.C. At 5:30.6. What does the woman want Jack to do?A. Relax his eyes.B. Read more books.C. Go shopping with her.听第6段材料，回答第7至9题。

深外高中园2022—2023学年度高一第一学期学段（二）考试英语试卷本试卷分选择题和非选择题两部分，共10页，满分为150分。

考试用时120分钟。

注意事项：1、答卷前，考生务必用黑色字迹的钢笔或签字笔将自己的姓名和学号填写在答题卡密封线内相应的位置上， 用2B铅笔将自己的学号填涂在答题卡上。

2、选择题每小题选出答案后，用2B铅笔把答题卡上对应题目的答案标号涂黑；如需改动，用橡皮擦干净 后，再选涂其他答案；不能答在试卷上。

3、非选择题必须用黑色字迹的钢笔或签字笔在答题卡上作答，答案必须写在答卷纸各题目指定区域内的相 应位置上，超出指定区域的答案无效；如需改动，先划掉原来的答案，然后再写上新的答案；不准使用铅 笔和涂改液。

不按以上要求作答的答案无效。

4、考生必须保持答题卡的整洁和平整。

第一部分听力（共两节，满分20分）第一节（共5小题；每小题1分，满分5分）听下面5段对话。

每段对话后有一个小题，从题中所给的A、B、C三个选项中选出最佳选项，并标在试卷 的相应位置。

听完每段对话后，你都有10秒钟的时间来回答有关小题和阅读下一小题。

每段对话仅读一遍。

1.What do we learn from the conversation?A.The man hates to lend his tools to other people.B.The man lost those tools.C.The man hasn’t finished working on the bookshelf.2.What are the two speakers talking about?A. A trip.B. A park.C. A cinema.3.What does the man mean?A.He would like to make an appointment for the woman.B.He thinks it worthwhile to try Santerbale’s.C.He knows a less expensive place for a haircut.4.What do we learn from this conversation?A The man wants to go to Los AngelesB The man wants to go to San Francisco.C There are no flights to Los Angeles for the rest of the day.5.What is the woman’s opinion of the research paper?A. Only a few changes should be made in it.B. It’s fine as it is.C. Major revisions are needed in it.第二节（共15小题：每小题1分，满分15分）听下面5段对话或独白。

广东省深圳外国语学校2023-2024 学年高一下学期开学检测考试英语试题学校:___________姓名：___________班级：___________考号：___________ 一、单项选择1．With her attention ________ on the book, the girl sat there quietly. A．to be fixed B．fix C．fixed D．fixing2．________to achieving a big, seemingly impossible goal reconnects us to a burning passion.A．Being committed B．Committed C．Committing D．To commit 3．The Chinese tech giant has launched its new operating system, ______an alternative app ecosystem to Google’s Android. A．creating B．to create C．having created D．creates4．The shop owner will get all these goods ordered ___________ to the customers today.A．to deliver B．delivering C．deliver D．delivered5．The girl is so proud that she can’t stand ___________ down upon. A．looking B．to look C．to be looked D．being looked 6．When he saw the mists rising from the river and the soft clouds the mountain tops, he was reduced to tears.A．being surrounded B．surrounded C．surrounding D．to surround 7．In the Chinese market, many foreign brands, ________ their reputations over decades, are facing new challenges due toCOVID-19.A．being developed B．developingC．having developed D．developed8．________ to think critically is an important skill today’s children will need for the future.A．Learn B．LearnedC．Learning D．Having learned9．When ______ different cultures, we often pay attention only to the differences without noticing many similarities.A．being compared B．comparingC．Compared D．having been compared10．（2015·江苏）Much time ________sitting at a desk, office workers are generally troubled by health problems.A．being spent B．having spentC．spent D．spending11．_________in Avebury, England, the monument is so large that it can only be seen from the sky.A．Located B．Locating C．Being located D．To locate 12．When Tom got home he saw a note on the table _______that don’t be discouraged, everything will turn out well soon. A．reading B．reads C．to read D．read13．_____ and caught the mouse.A．Up the cat jumped B．The cat up jumpedC．Up jumped the cat D．Jumped up the cat14．You say he works hard. ______ , and ______.A．So he does; so you do B．So he does; so do youC．So does he; so do you D．So does he; so you do15．So absorbed ________ the work that she often forgot to ________ her meals.A．had she been in; do B．she was in; makeC．was she in; take D．she had been in; have16．Hardly ________ his homework when he went out. A．finished he B．he had finished C．did he finish D．had he finished 17．It was not until near the end of the letter ________ she mentioned her own plan.A．that B．whereC．why D．when18．Was it in 1969 _____ the American astronaut succeeded ____ landing on the moonA．when; on B．that; on C．when; in D．that; in19．The computer was used in teaching. As a result, not only _____, but students became more interested in the lessons.A．sav ed was teachers’ energyB．was teachers’ energy savedC．teachers’ energy was savedD．was saved teachers’ energy20．________ who was wounded in the stomach.A．Among them were a soldier B．Among them was a soldier C．Among them a soldier was D．Among they was a soldier二、阅读理解There are many podcasts(播客)that teach English and you can listen to them anytime. Here is a list of some of the best podcasts that you must see.Learn English PodcastThis podcast has three levels. The first is for beginners, the second is for intermediates(中级学生)and the third is for upper intermediates. If a person wants to learn Business English, then episodes are also made for him. Every podcast is short but very informative. Worksheets(活页练习题)and vocabulary tasks are also included.Speaking BroadlyThis podcast is made for advanced learners. Explained through discussion and interviews, each episode has non-native English speakers and every recording also has expert feedback. You will see some common mistakes made by English learners and you can improve your English by learning from those mistakes.The English We SpeakThis podcast airs one episode daily and every episode is only three to four minutes, which talks about phrases and idioms. There are two people in each episode who communicate with each other. Whatever level you are, you will find it rewarding.Elementary PodcastThis podcast is mainly for beginners and intermediate level learners. The length of a podcast is around 25 minutes but you can pause it anytime and continue whenever you want. The hosts of each episode are different.21．Which podcast provides exercises going with it A．Speaking Broadly. B．Elementary Podcast.C．The English We Speak. D．Learn English Podcast.22．What do we know about Speaking BroadlyA．It records just expert speakers. B．It targets beginners.C．It presents some typical mistakes. D．It provides feedback from listeners.23．What do The English We Speak and Elementary Podcast have in commonA．They are both interactive. B．They cater for beginners. C．They have the same length. D．They share the same contents.I work with Volunteers for Wildlife, a rescue and educationorganization at Bailey Arboretum in Locust Valley. Trying to help injured, displaced or sick creatures can be heartbreaking; survival is never certain. However, when it works, it is simply beautiful.I got a rescue call from a woman in Muttontown. She had found a young owl(猫头鹰) on the ground. When I arrived, I saw a 2-to 3-week-old owl. It had already been placed in a carrier for safety.I examined the chick(雏鸟) and it seemed fine. If I could locate the nest, I might have been able to put it back, but no luck. My next work was to construct a nest and anchor it in a tree.The homeowner was very helpful. A wire basket was found. I put some pine branches into the basket to make this nest safe and comfortable. I placed the chick in the nest, and it quickly calmed down.Now all that was needed were the parents, but they were absent. I gave the homeowner a recording of the hunger screams of owl chicks. These advertise the presence of chicks to adults; they might also encourage our chick to start calling as well. I gave the owner as much information as possible and headed home to see what news the night might bring.A nervous night to be sure, but sometimes the spirits of nature smile on us all! The homeowner called to say that the parents had responded to the recordings. I drove over and saw the chick in thenest looking healthy and active. And it was accompanied in the nest by the greatest sight of all — LUNCH! The parents had done their duty and would probably continue to do so.24．What is unavoidable in the author’s rescue work according to paragraph 1A．Efforts made in vain.B．Getting injured in his work.C．Feeling uncertain about his future.D．Creatures forced out of their homes.25．Why was the author called to MuttontownA．To rescue a woman.B．To take care of a woman.C．To look at a baby owl.D．To cure a young owl.26．What made the chick calm downA．A new nest.B．Some food.C．A recording.D．Its parents.27．How would the author feel about the outcome of the event A．It’s unexpected.B．It’s beautiful.C．It’s humorous.D．It’s discouraging.You are given many opportunities in life to choose to be a victim or creator. When you choose to be a victim, the world is a cold and difficult place. “They” did things to you which caused all of your pain and suffering. “They” are wrong and bad, and life is terrible as long as “they” are around. Or you may blame yourself for all your problems, thus internalizing (内化) your victimization. The truth is, your life is likely to stay that way as long as you feel a need to blame yourself or others.Those who choose to be creators look at life quite differently. They know there are individuals who might like to control their lives, but they don’t let this get in the way. They know they have their weaknesses, yet they don’t blame themselves when they fail. Whatever happens, they have choice in the matter. They believe their dance with each sacred (神圣的) moment of life is a gift and that storms are a natural part of life which can bring the rain needed for emotional and spiritual growth.Victims and creators live in the same physical world and deal with many of the same physical realities, yet their experience of life is worlds apart. Victims relish (沉溺) in anger, guilt, and other emotions that cause others- -and even themselves--to feel likevictims, too. Creators consciously choose love, inspiration, and other qualities which inspire not only themselves, but all around them. Both victims and creators always have choice to determine the direction of their lives.In reality, all of us play the victim or the creator at various points in our lives. One person, on losing a job or a special relationship, may feel as if it is the end of the world and sink into terrible suffering for months, years, or even a lifetime. Another with the same experience may choose to first experience the grief, then accept the loss and soon move on to be a powerful creative force in his life.In every moment and every circumstance, you can choose to have filler, richer life by setting a clear intention to transform the victim within, and by inviting into your life the powerful creator that you are.28．What does the word “They” in paragraph 1 probably refer to A．People and things around you. B．Opportunities and problems. C．Creators and their choices. D．Victims and their sufferings. 29．According to Paragraph 2, creators ________.A．seem willing to experience failures in life B．possess the ability to predict future lifeC．handle ups and downs of life wisely D．have potential to createsomething new30．The examples mentioned in Paragraph 4 show that ________. A．different reactions to sufferings lead to different life paths. B．people need family support to deal with challengers in life. C．it takes creators quite a long time to get rid of their pains. D．one’s experiences determine his attitude toward life. 31．What is the author’s purpose in writing this passageA．To define victims and creators.B．To evaluate victims against creators.C．To explain the relationship between victims and creators. D．To suggest the transformation from victims to creators.Why do some men settle down to form families with the mothers of their children, and others don’t Biology plays a role. Work published by Lee Gettler of the University of Notre Dame, in Indiana, clarifies how testosterone, the principal male hormone (荷尔蒙), operates.Previous studies suggest that high levels of testosterone are bad for family life. Fathers with lower testosterone levels provide more child care while high-testosterone males are less likely to stick around. Dr. Gettler has shown something further. This is that a man’s adult testosterone level seems correlated with whether his father was present during his teenage years.His data come from a survey begun in the Philippines in 1983. This monitored the health and nutrition of 966 men enrolled as babies. It also collected extensive information on whether the fathers of these men were around and providing parental care in the households. It further documented whether participants got married, had children and whether they participated in child care. Crucially, it also measured their testosterone levels at the ages of 21, 26 and 30.Overall, Dr. Gettler and his colleagues found that on becoming fathers, men had lower testosterone levels if their own fathers had been involved in their care during their teenage years. It has two possible explanations. One is that it is directly genetic (基因的). The other is that teenage experience actually modulates (调节) testosterone levels. This explanation, which Dr. Gettler favors, could lead to high-testosterone men abandoning their sons, who thus become high-testosterone in their turn.He also found some of those in the survey whose fathers were absent during their adolescence, and who ended up with high levels of the hormone, did become caring fathers. Why this pattern should exist is an unanswered question. But a zoologist looking at these data might take it as an example of developmental plasticity (可塑性), in which the same genes produce different, butappropriate, outcomes in different circumstances.Dr. Gettler’s discovery throws a useful light on the problem of fatherless families,and how to try to end it.32．What is Gettler’s study mainly aboutA．Family life. B．Fathers’ roles.C．Adult testosterone. D．Child care.33．What can be learnt about Dr. Gettler’s studyA．It was conducted among babies.B．The finding is far from satisfactory.C．The data used were relatively reliable.D．It monitored the nutrition of participants.34．Why is the zoologist mentioned in the passageA．To suggest a follow-up study.B．To contradict Gettler’s ideas.C．To point out the study limitations.D．To give a possible explanation.35．Which of the following is a suitable title for the textA．Like Father, Like SonB．Caring Father, Happy SonC．Good Father, Good SonD．Love Me, Love My SonTechnology is here to stay. 36 . However, they are often unsure onhow to help children use technology responsibly and keep a balance between online and offline time. Here are some tips. Have a device contractHaving a device usage contract allows parents and children to work through what responsible technology usage looks like in your family and ensure that everyone is aware. 37 . Kids are more likely to make sense of the reasons you have for restriction.38Although this tip seems like common sense, it is often difficult due to the demand of work and the expectation of being constantly connected. By ensuring you build offline time into your own day and communicate that with your children, they will see the value and benefits. Whether you are reading a book or just taking a walk, letting your children be aware of your offline actions will encourage them to do the same!Encourage non-tech activitiesOne great way to keep kids off their screens is to ensure that they have other activities to fill their time. 39 . These activities are also great ways to help children to develop their social skills and confidence.Tech-free family timeOnce a week, pencil-in a “tech-free family time” in your schedule. Itcan be a meal or trip. To help increase the success of outings, try designing special activities, i. e., going to the beach to build a sand castle that looks the same as a photo you have found online. 40 A．Model good technology useB．Communicate with childrenC．A little extra planning goes a long wayD．The contract is helpful to the settlement of conflicts E．Parents are seeing more technology in their homes and jobs F．Also, drafting the contract together promotes understanding G．This can come in a variety of forms: soccer, fencing and more 三、完形填空My first caregiving experience involved driving 180 miles every day to see my grandmother who was terminally ill. I was certainly 41 as the weeks turned into months, but the desire to 42 my grandmother in her last days was overwhelming (无法抗拒的). Years later, my 87-year-old father required more 43 skills than I could provide. As he lived 700 miles away from me, I deeply 44 that I couldn’t take care of him myself, but I though t my nightly phone calls, filled with laughter and family news, provided him with 45 support.Then, 46 , because of cancer, I became the one who needed 47 . Friends provided meals, house cleaning, and rides to appointments.The gratitude I felt for these acts of 48 was beyond words. It was also because of their thoughtfulness that I could focus all my energy on healing (治愈) my body and mind.Soon afterwards, in trying to find a meaningful purpose, I 49 the idea of offering assistance to other caregivers. I was 50 with both sides of the struggle, and this 51 me to pay it forward for the incredible amount of support I had received.A(n) 52 arose when a caregiver I knew for years was unable to travel to her winter home in Florida. While recovering from surgery, she was 53 to drive. When she asked me to be the driver, I didn’t 54 , so we headed south on an adventure.Now, due to the pandemic, I have to suspend the program, but I look forward to 55 my journey of caring for caregivers soon. I welcome the chance to lift the burden off their shoulders, even if it’s for just a minute.41．A．relieved B．delighted C．frustrated D．exhausted 42．A．rescue B．comfort C．please D．protect 43．A．communication B．survival C．nursing D．working 44．A．regretted B．assumed C．feared D．appreciated 45．A．professional B．physical C．financial D．emotional 46．A．unfortunately B．gradually C．eventually D．surprisingly 47．A．encouragement B．attention C．care D．guidance48．A．bravery B．modesty C．honesty D．kindness 49．A．reflected on B．came upon C．went over D．focused on 50．A．faced B．occupied C．acquainted D．associated 51．A．allowed B．required C．advised D．forced 52．A．problem B．crisis C．opportunity D．emergency 53．A．forbidden B．expected C．supposed D．determined 54．A．respond B．hesitate C．struggle D．compromise 55．A．extending B．planning C．finishing D．continuing四、语法填空阅读下面短文，在空白处填入1个适当的单词或括号内单词的正确形式。

深圳外国语学校2024届高三第一次月考试题数学本试卷分选择题和非选择题两部分，共4页，满分150分，考试用时120分钟。

注意事项：1．答题前，考生务必用黑色字迹的钢笔或签字笔将自己的姓名、班级、座位号等相关信息填写在答题卷指定区域内。

2．选择题每小题选出答案后，用2B 铅笔把答题卷上对应题目的答案标号涂黑；如需改动，用橡皮擦干净后，再选涂其它答案；不能答在试卷上。

3．非选择题必须用黑色字迹的钢笔或签字笔作答，答案必须写在答题卷各题目指定区域内的相应位置上；如需改动，先划掉原来的答案，然后再写上新的答案；不准使用铅笔和涂改液.不按以上要求作答的答案无效。

4．考生必须保持答题卷的整洁第一部分选择题(共60分)一、单选题(本题共8小题，每小题5分，共40分．每小题给出的四个选项中，只有一个选项是符合题目要求的)1.已知全集U =R ，集合A ={x x ≥4或x ≤0}，B ={x x >4或x ≤-2}，则图中阴影部分表示的集合为()A ．-2,0B ．-2,0C ．-2,0 ∪4D ．-2,0 ∪42.若复数z 所对应的点在第四象限，且满足z 2-2z +2=0，则z 2=()A.1+iB.1-iC.-2iD.2i3.已知a ⋅b =-24，a +2b =(-5,2)，若a 与b 模相等，则a =( ).A.3B.4C.5D.64.探照灯反射镜的纵断面是抛物线的一部分，光源放在焦点F 处．已知灯口直径为60cm ，光源距灯口的深度为40cm ，则光源到反射镜的顶点的距离为A.5cmB.10cmC.15cmD.20cm5.设函数f x =a -1 x x -b +1 为奇函数且在R 上为减函数，则关于a ,b 的值表述正确的是()A.a >1,b =1B.a >1,b <1C.a <1,b =1D.a <1,b >16.定义函数迭代：f 0x =x f 1 x =f x f 2 x =f f x ⋯f n +1x =f fnx已知f x =3x +2，则f nx =()A.3n x +3n -1B.3n x +3n +1C.3nx +3n -1D.3n x -3n +17.如图，F 1､F 2是双曲线C ：x 2a 2-y 2b2=1a >0,b >0 的左､右焦点，过F 2的直线与双曲线C 交于A ､B 两点.若A 是BF 2中点且BF 1⊥BF 2则该双曲线的渐近线方程为()A.y =±23xB.y =±22xC.y =±3xD.y =±2x8.若∃m ∈R ，对于∀x ∈a ,b 恒有2m 2-22sin x +π4 ⋅m +sin2x ≤0，则b -a 的最大值是()A.3π4B.πC.4π3D.2π二、多选题(本题共4小题，每小题5分，共20分.在每小题给出的选项中，有多项符合题目要求，全部选对的得5分，部分选对的得2分，有选错的得0分)9.已知函数f (x )和g (x )分别为奇函数和偶函数，且f (x )+g (x )=2x ，则()A.f (x )-g (x )=2-xB.f (x )在定义域(-∞,+∞)上单调递增C.f (x )的导函数f (x )≥1D.g (x )≥110.给出下列说法，其中正确的是()A.数据0，1，2，4的极差与中位数之积为6B.已知一组数据x 1,x 2,⋯,x n 的方差是5，则数据4x 1-1,4x 2-1,⋯,4x n -1的方差是20C.已知一组数据x 1,x 2,⋯,x n 的方差为0，则此组数据的众数唯一D.已知一组不完全相同的数据x 1,x 2,⋯,x n 的平均数为x 0，在这组数据中加入一个数x 0后得到一组新数据x 0,x 1,x 2,⋯,x n ，其平均数为x ，则x=x 011.已知函数f x 定义域为R ，f x +1 是奇函数，g x =1-x f x ，函数g x 在1,+∞ 上递增，则下列命题为真命题的是()A.f -x -1 =-f x +1B.函数g x 在-∞,1 上递减C.若a <2-b <1，则g 1 <g b <g aD.若g a >g a +1 ，则a <1212.如图AD 与BC 分别为圆台上下底面直径，AD ⎳BC ，若AB =3，AD =2，BC =4，则()A.圆台的母线与底面所成的角的正切值为22B.圆台的全面积为14πC.圆台的外接球(上下底面圆周都在球面上)的半径为2D.从点A 经过圆台的表面到点C 的最短距离为33第二部分非选择题(90分)三、填空题(本题共4小题，每小题5分，共20分)13.钥匙掉了，掉在宿舍里､掉在教室里､掉在路上的概率分别是50%、30%和20%，而掉在上述三处被找到的概率分别是0.8、0.3和0.1，则找到钥匙的概率为.14.已知圆柱体的底面半径为32cm ，高为5πcm ，一只蜗牛从圆柱体底部开始爬行，绕圆柱体4圈到达顶部，则蜗牛爬行的最短路径长为．15.测量地震级别的里氏是地震强度(即地震释放的能量)的常用对数值．显然级别越高，地震的强度也越高，如日本1923年地震是8.9级，旧金山1906年地震是8.3级，问日本1923年地震强度是8.3级的倍．(lg2≈0.3)16.已知椭圆E 的中心为O ，E 上存在两点A ，B ，满足△OAB 是以半焦距为边长的正三角形，则E 的离心率为.四、解答题(本题共6小题，共70分，其中17题10分，其余各题12分.解答应写出文字说明、证明过程或演算步骤)17.已知数列a n 满足a 1=1，a n +13a n =1+1n ．(1)求数列a n 的通项公式；(2)求数列a n 的前n 项和S n ．18.如图，多面体ABCDEF 中，四边形ABCD 为矩形，二面角A -CD -F 的大小为45°，DE ⎳CF ，CD ⊥DE ，AD =2，DC =3.(1)求证：BF ⎳平面ADE ；(2)求直线AC 与平面CDEF 所成角的正弦值.19.已知抛物线C 的焦点F 到准线l 的距离为2.(1)求抛物线的标准方程；(2)过焦点F 的直线(斜率存在且不为0)交抛物线C 于A ,B 两点，线段AB 的中垂线交抛物线的对称轴于点P ，求FPAB.20.如图，某景区绿化规划中，有一块等腰直角三角形空地ABC ，∠BAC =π2，BC =30m ，Q 为BC 上一点，满足BQ =2CQ .现欲在边界AB ，AC (不包括端点)上分别选取M ，N 两点，并在四边形AMQN 区域内种植花卉，且∠MQN =π2，设∠NQC =θ.(1)证明：QMQN =2；(2)tan θ为何值时，花卉种植的面积占整个空地面积的一半？21.高尔顿板又称豆机、梅花机等，是英国生物统计学家高尔顿设计用来研究随机现象的模型．如图所示的高尔顿板为一块木板自上而下钉着6层圆柱形小木块，最顶层有2个小木块，以下各层小木块的个数依次递增，各层小木块互相平行但相互错开，小木块之间留有适当的空隙作为通道，前面挡有一块透明玻璃．让小球从高尔顿板上方的通道口落下，小球在下落过程中与层层小木块碰撞，且等可能向左或者向右滚下，最后落入高尔顿板下方从左至右编号为1，2，⋯，6的球槽内．(1)某商店将该高尔顿板改良成游戏机，针对某商品推出促销活动．凡是入店购买该商品一件，就可以获得一次游戏机会．若小球落入X 号球槽，该商品可立减Y 元，其中Y =20-5X ．若该商品的成本价是10元，从期望的角度考虑，为保证该商品总体能盈利，求该商品的最低定价．(结果取整数)(2)将79个小球依次从高尔顿板上方的通道口落下，试问3号球槽中落入多少个小球的概率最大？附：设随机变量ξ~B (n ,p )，则ξ的分布列为P (ξ=k )=C k n p k (1-p )n -k ，k =0,1,2,⋯,n ．P (ξ=k )P (ξ=k -1)=C k n p k(1-p )n -k C k -1n p k -1(1-p )n -k +1=1+(n +1)p -kk (1-p )．22.设函数f x =-x ln x+ax2+x a∈R.(1)若函数f x 有两个不同的极值点，求实数a的取值范围；(2)若a=1，k∈N*，g x =x2+2x，当x>2时，不等式2k x-2+f x <g x 恒成立，试求正整数k的最大值.深圳外国语学校2024届高三入学测试数学试卷参考答案选择题：共12小题，每小题5分，满分60分题号123456789101112答案DCCACAABBDACDBCDABD1.D【详解】因为A ={x x ≥4或x ≤0}，B ={x x >4或x ≤-2}，所以A ∪B ={x x ≥4或x ≤0}∪{x x >4或x ≤-2}={x x ≥4或x ≤0}，A ∩B ={x x ≥4或x ≤0}∩{x x >4或x ≤-2}={x x >4或x ≤-2}.由题意可知阴影部分对于的集合为∁U A ∩B ∩A ∪B ，所以∁U A ∩B ={x -2<x ≤4 ，∁U A ∩B ∩A ∪B ={x -2<x ≤0或x =4}.故选：D .2.C【详解】因为复数z 满足：z 2-2z +2=0，即(z -1)2=-1，故z =1+i 或z =1-i ，因为复数z 所对应的点在第四象限，故复数z =1-i ，所以z 2=-2i. 故选:C .3.C故a +2b 2=a 2+4b 2+4a ⋅b =29，而又已知a ⋅b =-24，且a =b ，所以a 2+4a 2-96=29，解得a =5.故选：C4.A【详解】以抛物线的顶点为坐标原点建立平面直角坐标系如下图所示，设F p2,0，则抛物线上一点的坐标为p 2+40,30，代入抛物线方程y 2=2px p >0 得302=2p p 2+40 ，解得p =10,p 2=5，所以光源到反射镜的顶点的距离为5cm.故选：A5.C【详解】因为函数f x =a -1 x x -b +1 为R 上的奇函数，且递减，所以a -1≠0且f -1 =-f 1 ，即-a -1 -b =-a -1 2-b ，所以-b =2-b ，解得b =1，经检验符合题意，故f x =a -1 x x =a -1 x2,x ≥0-a -1 x 2,x <0因为函数f x =a -1 x x 在R 上为减函数，所以a -1<0，所以a <1.故选：C .6.A【详解】对于∀x 0∈R ，设a n =f nx 0 n ∈N ∗，则a 1=f 1x 0 =f x 0 =3x 0+2，且a n +1=3a n +2，所以a n +1+1=3a n +3=3a n +1 ，所以a n +1 是以3x 0+3为首项，公比为3的等比数列.a n +1=f nx 0 +1=3x 0+3 3n -1=3n x 0+3n ，即f nx 0 =3n x 0+3n -1.所以f nx =3n x +3n -1，故选：A .7.A【详解】设AB =AF 2 =m ,AF 1 =AF 2 +2a =m +2a ,BF 1 =BF 2 -2a =2m -2a ，BF 12+BA 2=AF 1 2,BF 1 2+BF 2 2=F 1F 2 2,2m -2a 2+m 2=m +2a 2①，2m -2a 2+4m 2=4c 2②,由①可得m =3a ,代入②式化简得：13a 2=c 2,∴12a 2=b 2,∴ba=23,所以双曲线的渐近线方程为y =±bax =±23x .故选：A8.B【详解】由2m 2-22sin x +π4⋅m +sin2x ≤0，得m 2-sin x +cos x ⋅m +sin x ⋅cos x ≤0，即m -sin x m -cos x ≤0,由几何意义可知，函数y =m 的图像在函数y =sin x ，y =cos x 的图像之间，如下图所示，-22≤m ≤22，要使b -a 达到最大，仅需要m =-22或m =22，此时b -a =π4--3π4=π.故选：B .9.BD【详解】由f (x )+g (x )=2x 得f (-x )+g (-x )=2-x ，由于函数f (x )和g (x )分别为奇函数和偶函数，所以-f (x )+g (x )=2-x，因此f x =2x -2-x 2,g x =2x +2-x 2，对于A , f (x )-g (x )=-2-x ,故A 错误，对于B ，由于函数y =2x 在(-∞,+∞)单调递增，y =2-x在(-∞,+∞)单调递减，所以f x =2x -2-x 2在(-∞,+∞)单调递增，故B 正确，对于C ，fx =2x ln2+2-x ln22=2x +2-xln22≥22x ×2-x ln22=ln2,当且仅当x =0时取等号，而ln2<1，所以C 错误，对于D ，g x =2x +2-x 2≥22x ×2-x2=1，当且仅当x =0时取等号，所以D 正确，故选：BD 10.ACD【详解】对于A ，极差为4-0=4，中位数为1+22=32，所以极差与中位数之积为4×32=6，A 对；对于B ，根据方差的性质可知，数据4x 1-1,4x 2-1,⋯,4x n -1的方差是42×5=80，B 错；对于C ，由方差s 2=1n x 1-x 2+x 2-x 2+⋯x n -x 2 =0，可得x 1=x 2=⋯=x n =x，即此组数据众数唯一，C 对；对于D ，∵x 1+x 2+⋯+x n n =x 0,∴x 1+x 2+⋯+x n =nx 0，∴x 0+x 1+x 2+⋯+x n n +1=x 0+nx 0n +1=x 0，D 对.故选：ACD11.BCD【详解】对于A ，因为f x +1 是奇函数，所以f -x +1 =-f x +1 ，故A 错误；因为f x +1 是奇函数，所以y =f x 的图象关于点1,0 对称，即有f x =-f 2-x ，所以g 2-x =1-2-x f 2-x =x -1 f 2-x =(1-x )f (x )=g x ，所以y =g x 的图象关于直线x =1对称，函数g x 在x ∈1,+∞ 上单调递增，所以g x 在x ∈-∞,1 上单调递减，故B 正确；因为a <2-b <1，所以g 1 <g 2-b <g a ，即g 1 <g b <g a ，故C 正确；因为g a >g a +1 ，且a <a +1，由函数y =g x 的图象关于直线x =1对称，得a +a +12<1，解得a <12，故C 正确.故选：BCD .12.ABD【详解】取圆台的轴截面ABCD ，设AD 、BC 的中点分别为O 1、O 2，连接O 1O 2，分别过点A 、D 在平面ABCD 内作AE ⊥BC ，DF ⊥BC ，垂足分别为点E 、F ，由题意可知，O 1O 2与圆台的底面垂直，易知四边形ABCD 为等腰梯形，且AB =CD =3，AD =2，BC =4，在△ABE 和△DCF 中，AB =DC ，∠ABE =∠DCF ，∠AEB =∠DFC =90°，所以，△ABE ≌△DCF ，所以，BE =CF ，因为AD ⎳BC ，AE ⊥BC ，DF ⊥BC ，则四边形ADFE 为矩形，且EF =CD =2，同理可证四边形AEO 2O 1为矩形，则O 1O 2=AE ，且AE ⎳O 1O 2，所以，AE 与圆台的底面垂直，则圆台的母线与底面所成的角为∠ABE ，所以，BE =CF =AB -EF 2=4-22=1，则AE =AB 2-BE 2=32-1=22，所以，tan ∠ABE =AEBE=22，A 对；对于B 选项，圆台的全面积为π×12+π×22+π×1+2 ×3=14π，B 对；对于C 选项，易知圆台的外接球球心在梯形ABCD 内，且CE =BC -BE =4-1=3，由勾股定理可得AC =AE 2+CE 2=8+9=17，且sin ∠ABE =AE AB=223，所以，圆台的外接球直径为2R =AC sin ∠ABE =17223=3344，则R =3348，B 错；对于C 选项，将圆台沿着轴截面ABCD 切开，将圆台的侧面的一半展开如下图所示：延长BA 、DC 交于点M ，在圆台的轴截面等腰梯形ABCD 中，AB ⎳CD 且AB =12CD ，易知A 、D 分别为BM 、CM 的中点，所以，AM =DM =AB =3，设∠AMD =θ，则AD =3θ=π，则θ=π3，在△ACM 中，AM =3，CM =6，∠AMD =π3，由余弦定理可得AC =AM 2+CM 2-2AM ⋅CM cos π332+62-2×3×6×12=33，因此，从点A 经过圆台的表面到点C 的最短距离为33，D 对.故选：ABD .三、填空题：共4小题，每小题5分，满分20分．13.0.5114. 13π(cm )15. 416. 3-1或6313.0.51【详解】记事件A 1为“钥匙掉在宿舍里”，A 2为“钥匙掉在教室里”，A 3为“钥匙掉在宿舍里”，事件B 为“找到钥匙”，由全概率公式得P (B )=P (A 1)P B A 1 +P (A 2)P B A 2 +P (A 3)P B A 3 =0.5×0.8+0.3×0.3+0.2×0.1=0.5114.13π(cm )【详解】根据题意，从圆柱底部M 点绕圆柱体的侧面旋转4圈到达顶部的N 点，沿MN 将侧面展开后，最短路程，如图所示，其中矩形的高等于圆柱的高5πcm ，矩形的宽等于圆柱的底面圆的周长的4倍，即4×2π×32=12πcm ，所以蜗牛爬行的最短路径为MN =(5π)2+(12π)2=13π(cm ).故答案为：13π(cm ).15.4【详解】设地震强度为x ，则地震级别为f (x )=lg x ，由题意可令lg x =8.9,lg t =8.3，则lg x -lg t =8.9-8.3=0.6，由于lg2≈0.3，故lg x -lg t =2lg2=lg4,∴lg x t =lg4,xt=4，即日本1923年地震强度是8.3级的4倍，故答案为：416.3-1或63【详解】不妨设椭圆方程为x 2a 2+y 2b2=1(a >b >0)，因为△OAB 是以半焦距为边长的正三角形，根据椭圆的对称性，可知AB 平行于x 轴或AB 平行于y 轴；当AB 平行于x 轴时，A ,B 关于y 轴对称，不妨设点A 在第一象限，所以∠AOx =60°，OA =c ，所以A c 2,3c 2 ，所以c 24a 2+3c 24b2=1，即c 2(a 2-c 2)+3a 2c 2=4a 2(a 2-c 2)，所以c 4-8a 2c 2+4a 4=0，即e 4-8e 2+4=0，解得e 2=4-23或e 2=4+23(因为0<e <1，故舍去)，所以e =3-1；当AB 平行于y 轴时，A ,B 关于x 轴对称，所以∠AOx =30°，OA =c ，不妨设点A 在第一象限，所以A 3c 2,c 2 ，所以3c 24a 2+c 24b2=1，即3c 2(a 2-c 2)+a 2c 2=4a 2(a 2-c 2)，即3c 4-8a 2c 2+4a 4=0，所以3e 4-8e 2+4=0，而0<e <1，解得e 2=23或e 2=2(舍去)，故e =63，所以椭圆的离心率为3-1或63，故答案为：3-1或63四．解答题(共6小题)17.【详解】(1)由a n +13a n =1+1n ，得a n +1n +1=3×a n n，------------2分又a 11=1，∴a n n 是以1为首项，3为公比的等比数列，------3分∴an n=3n -1，a n =n ×3n -1，即数列a n 的通项公式为a n =n ×3n -1.------5分(2)由(1)知，a n =n ×3n -1，则S n =1×30+2×31+⋅⋅⋅+n ×3n -11--------------6分1×3得3S n =1×31+2×32+⋅⋅⋅+n ×3n 2-----------7分1-2得-2S n =1+31+32+⋅⋅⋅+3n -1-n ×3n --------------8分=1-3n 1-3-n ×3n =3n -12-n ×3n ------------------------9分故S n =2n -1 ×3n+14．---------------10分18.【详解】(1)证明：因为四边形ABCD 是矩形，所以，BC ⎳AD ，因为BC ⊂平面BCF ，AD ⊄平面BCF ，所以AD ⎳平面BCF ， --------------------2分因为DE ⎳CF ，CF ⊂平面BCF ，DE ⊄平面BCF ，所以DE ⎳平面BCF ， ----------4分因为AD ∩DE =D ，AD 、DE ⊂平面ADE ，则平面BCF ⎳平面ADE ，---------------5分因为BF ⊂平面BCF ，所以，BF ⎳平面ADE .------------------------------6分(2)解：因为CD ⊥AD ，CD ⊥DE ，所以，二面角A -CD -F 的平面角为∠ADE ，----------7分由题意可得∠ADE =45°，又因为AD ∩DE =D ，AD 、DE ⊂平面ADE ，所以，CD ⊥平面ADE ，过点A 在平面ADE 内作AO ⊥DE ，垂足为点O ，因为AO ⊂平面ADE ，所以CD ⊥AO ，-----------------8分又因为CD ∩DE =D ，CD 、DE ⊂平面CDEF ，所以AO ⊥平面CDEF ，连接CO ，所以直线AC 与平面CDEF 所成角为∠ACO ， -----9分因为CD ⊥AD ，AD =2，DC =3，则AC =AD 2+DC 2=22+32=13，因为AO ⊥DE ，则AO =AD sin ∠ADE =2×22=2，-----------------11分所以sin ∠ACO =AO AC =213=2613.直线AC 与平面CDEF 所成角的正弦值为2613-------12分19.【详解】(1)因为抛物线C 的焦点F 到准线l 的距离为2，所以p =2，----------2分根据建系方案的不同，抛物线的标准方程有四种可能，分别是y 2=4x ，y 2=-4x ，x 2=4y ，x 2=-4y .------------------4分(2)在平面直角坐标系中，抛物线的位置并不影响FP AB的取值，因此不妨取抛物线的方程为y 2=4x ，此时焦点F 1,0 ，根据题意，直线AB 的斜率存在且不为0，因此设直线AB 的方程为x =my +1，---5分与抛物线y 2=4x 联立，得关于y 的一元二次方程y 2-4my -4=0，-----------6分则Δ=16m 2+16>0，设A x 1,y 1 、B x 2,y 2 ，则y 1+y 2=4m ，y 1y 2=-4，y 1-y 2 =16m 2+16，-----------7分x 1+x 2=m y 1+y 2 +2=4m 2+2，-----------------------8分则AB =1+m 2y 1-y 2 =41+m 2 ，--------------------9分线段AB 的中点坐标为2m 2+1,2m ，中垂线方程为y -2m =-m x -2m 2-1 ，令y =0，解得x =3+2m 2，即中垂线与x 轴交于P 3+2m 2,0 ，---------10分所以FP =2+2m 2，------------------------11分则FP AB=12.-------------------------------12分20.【详解】(1)由题意得BQ =20m ，QC =10m ，∠B =∠C =π4，∵∠MQN =π2，∠BAC =π2，四边形内角和等于2π，所以∠AMQ +∠ANQ =π，又∠AMQ +∠BMQ =π,∠ANQ +∠CNQ =π，--------------------1分∴∠CNQ +∠BMQ =π，sin ∠CNQ =sin ∠BMQ ，-------------------------2分在△BMQ 中，由正弦定理得MQ sin B =BQ sin ∠BMQ，-------------------------3分在△CQN 中，由正弦定理得NQ sin C =CQ sin ∠CNQ，--------------------4分∴MQ NQ =BQ QC=2，证毕；-------------------------5分(2)由题意得AB =AC =152m ，故S △ABC =12AB ⋅AC =225m 2，-----------6分∵∠MQN =π2，∠NQC =θ，∴∠BQM =π2-θ，∴∠C =π4，∴∠QNC =3π4-θ，-------------7分设QN =xm ，则QM =2xm ，在△CQN 中，由正弦定理得NQ sin C =CQ sin ∠CNQ，即x sin π4=10sin 3π4-θ ，解得x =10sin π4sin 3π4-θ =52sin 3π4-θ ①，-------8分由三角形面积公式得S △CNQ =12CQ ⋅QN sin ∠CQN =5x sin θ，S △BMQ =12BQ ⋅QM sin ∠BQM =20x sin π2-θ =20x cos θ，--------------------9分故S △CNQ +S △BMQ =5x sin θ+20x cos θ=12S △ABC =2252，∴x =452sin θ+4cos θ②，--------10分由①②得52sin 3π4-θ =452sin θ+4cos θ ，化简得sin θ+4cos θsin θ+cos θ=92，-----------11分分子分母同除以cos θ得tan θ+4tan θ+1=92，解得tan θ=-17---------12分21.【详解】(1)X 的取值可能为1，2，3，4，5，6．--------1分P (X =1)=P (X =6)=12 5=132，P (X =2)=P (X =5)=C 15×12×12 4=532，P (X =3)=P (X =4)=C 25×12 2×12 3=516．------------------2分因为Y =|20-5X |，所以Y 的取值可能为0，5，10，15．P (Y =0)=P (X =4)=516，P (Y =5)=P (X =3)+P (X =5)=1532，P (Y =10)=P (X =2)+P (X =6)=316，P (Y =15)=P (X =1)=132．----------3分Y 的分布列为Y051015P 5161532316132E (Y )=0×516+5×1532+10×316+15×132=7516≈4.7，----------------------4分则顾客玩一次游戏，立减金额的均值约为4.7元，又该商品成本价是10元，所以该商品的最低定价约为15元．----------------------------5分(2)由(1)得P (X =3)=516．进行79次试验，设小球落入3号球槽的个数为ξ，则ξ~B 79,516．----------6分P (ξ=k )P (ξ=k -1)=1+(79+1)×516-k k 1-516 =1+25-k 11k 16．------8分当k <25时，P (ξ=k )P (ξ=k -1)>1，即P (ξ=k )>P (ξ=k -1)；------------9分当k =25时，P (ξ=k )P (ξ=k -1)=1，即P (ξ=k )=P (ξ=k -1)；-----------10分当k >25时，P (ξ=k )P (ξ=k -1)<1，即P (ξ=k )<P (ξ=k -1)．------------------11分所以当k =25时，P (ξ=25)=P (ξ=24)，此时这两项概率均为最大值．故3号球槽中落入24或25个小球的概率最大．--------------------------12分22.【详解】(1)由题意可知，f x 的定义域为0,+∞ ，f x =-ln x +2ax .令f x =0，可得2a =ln x x ，-------------1分令ℎx =ln x x x >0 ，ℎ x =1-ln x x2，令ℎ x =0得x =e ，----------2分当0<x <e 时，ℎ x >0，当x >e 时，ℎ x <0，可知ℎx 在0,e 上单调递增，在e ,+∞ 上单调递减，--------3分所以ℎx max =ℎe =1e，又当0<x <1时，ℎx <0，当x >1时，ℎx >0，根据以上信息，作出ℎx 的大致图象，-----------4分则由题意可知y =2a 与函数ℎx 的图象有两个不同的交点，∴2a ∈0,1e ，∴a ∈0,12e.-----------------5分(2)当a =1时，f x =-x ln x +x 2+x ，由2k x -2 +f x <g x 得2k x -2 <x ln x +x ，因为x >2，所以2k <x ln x +x x -2.----------------------------------6分设F x =x ln x +x x -2x >2 ，则F x =x -4-2ln x x -22，------------7分令m x =x -4-2ln x x >2 ，则m x =1-2x>0，所以m x 在2,+∞ 上单调递增，------------------------------------8分又m 8 =4-2ln8<4-2ln e 2=0，m 10 =6-2ln10>6-2ln e 3=0，所以m x 在8,10 上有唯一的零点x 0，即x 0-4-2ln x 0=0，--------------9分当2<x <x 0时，m x <0，即F x <0，当x >x 0时，m x >0，即F x >0，所以F x min =F x 0 =x 0ln x 0+x 0x 0-2=x 01+x 0-42 x 0-2=x 02，---------------------10分所以2k <x 02，又x 0∈8,10 ，所以x 02∈4,5 ，-------------11分又k ∈N *，所以k 的最大值为2.----------------12分。

2020-2021学年深圳市外国语高级中学高一入学考试
物理模拟试卷解析版
一、解答题（共9小题，满分36分）
1．（4分）下列物理量中，不是矢量的是（）
A．加速度B．位移C．瞬时速度D．路程
【解答】解：加速度、位移和瞬时速度都是既有大小又有方向的矢量，而路程只有大小没有方向，是标量，故ABC错误，D正确。

故选：D。

2．（4分）在杭宁高速公路上，分别有图示的甲、乙两块告示牌，告示牌上面数字的意思是（）
A．甲是指位移，乙是平均速度
B．甲是指路程，乙是平均速度
C．甲是指位移，乙是瞬时速度
D．甲是指路程，乙是瞬时速度
【解答】解：告示牌甲是量程牌，表示路程。

限速是指瞬时速度不能超过多大，告示牌乙上面的数字是瞬时速度。

故选：D。

3．（4分）皮球从3m高处落下，被地板弹回，在距地面1m高处被接住，则皮球通过的路程和位移的大小分别是（）
A．4m、4m B．3m、1m C．3m、2m D．4m、2m
【解答】解：位移是指从初位置到末位置的有向线段，所以此时物体的位移的大小是：x ＝3m﹣1m＝2m
路程是指物体所经过的路径的长度，此时的路程为：s＝3m+1m＝4m。

故选：D。

4．（4分）如图所示的时间轴，下列关于时刻和时间的说法中正确的是（）
第 1 页共7 页。

深圳外国语学校高中园2025届高三年级第二次调研考试数学答案1．D 2．B 3．D 4．B 5．C 6．C 7．B【详解】当x <1时，则f (x )=−ax 2+2ax −a +3=−a (x −1)2+3， 且a >0，所以f (x )=−a (x −1)2+3<3，若函数()f x 的值域为R ，可知当1x ≥时，则f (x )=a x +a 的值域包含[)3,+∞， 若0<a <1，则f (x )=a x +a 在1,+∞)内单调递减， 可得f (x )≤f (1)=2a ，不合题意；若a >1，则f (x )=a x +a 在1,+∞)内单调递增， 可得f (x )≥f (1)=2a ，则2a ≤3，解得1<a ≤32；综上所述：实数a 的取值范围是31,2⎛⎤⎥⎝⎦.故选：B. 8．A【详解】由()f x 的图象关于点(1,0)对称可得f (x +2)=−f (−x )． 由f (x +1)+f (x +2)=0，可得f (x +1)=−f (x +2)=f (−x )， 故函数()f x 的图象关于直线12x =对称， 且f (x +2)=−f (x +1)=−(−f (x ))=f (x )，得()f x 的周期为2．当10,2x ⎡⎤∈⎢⎥⎣⎦时，()()()()()22221222log 31log 31log 312111x x f x x x x x x x +−=++=++=+−++++， ()f x 单调递增，且f (13)=32，则f (43)=f (13+1)=−f (13)=−32，f (53)=f (2−13)=−f (13)=−32，画出()f x 在一个周期内的大致图象如图所示： 当012m <+<时，结合图象可得45133m <+<，即1233m <<．故实数m 的取值范围为()122,233k k k ⎛⎫++∈ ⎪⎝⎭Z ．故选：A. 9．ABD 10．AD 11．BCD【详解】对于A ，若函数()f x 在R 上单调递增，则{−a2≥0−2a ≤1−a ，解得a ∈[−1,0]，故A错误；对于B ，若函数()f x 有3个零点，则当0x <时，2(2)x ax a f x −−=−有2个零点12,x x ， 所以{Δ=a 2−8a >0x 1+x 2=−a <0x 1x 2=2a >0，解得8a >，当0x ≥时，f(x)=e x −a 有1个零点，则1a ≥， 所以()8,a ∈+∞，故B 正确；对于C ，设函数()f x 的3个零点分别是1x ，2x ，3x （123x x x <<）， 由B 知，()8,a ∈+∞，12x x a +=−，令e 0()x f a x =−=，解得ln x a =，即3ln x a =，设1231l 3)13n (a a h a x x x −+==−−，()8,a ∈+∞，得()h a 在()8,+∞上单调递减，所以()(),8ln 2h a ∈−∞−−，故C 正确；对于D ，当[)0,1x ∈时，()e x f x a =−单调递增，[)()1,e f x a a ∈−−， 当()1,0x ∈−时，2(2)x ax a f x −−=−，对称轴为直线2ax =−， ①当122a −≥−，即1a ≤时，()(1)1211f x f a a a a <−=−+−=−−<−，无最小值； ②当122a −<−，即1a >时，((2)0)a f x f <=−， 若()f x 有最小值，则12a a −≤−，解得1a ≤−，与1a >矛盾，故无最小值； 综上任意实数a ，函数()f x 在()1,1−内无最小值，故D 正确； 故选：BCD ． 12．(-1，2)13．1− 14．2±【详解】由题意()12y f x =+为奇函数， 所以()11[()]22f x f x −+=−+，则112222xx n n m m −=+++−−， 所以202(2221)(12)(2)122(12)(2)10x x x x x x x x xn n n m m m m m m m ⋅+⋅+++=⋅+++⋅++++⇒=⋅， 所以22()2(21)20x x n m m mn n m ++++⋅++=恒成立， 故2012101m n m m mn n +==−⎧⎧⇒⎨⎨++==⎩⎩或11m n =⎧⎨=−⎩，所以2m n −=±.故答案为：2±。

广东省深圳市福田外国语高级中学2022-2023学年高一上学期入学考试英语试题学校:___________姓名：___________班级：___________考号：___________一、完形填空When I first arrived in Santiago, Chile, and took a walk around the city center, one of the first things I noticed was how many street dogs there were.On every corner there was a sleeping 1 . At every traffic light there was a dog 2 to cross. By every shop there was a dog waiting for 3 . At first I was 4 as I thought they might be 5 or unfriendly. However, I have been here for more than a year now and every street dog I have seen has been quiet and 6 .The dogs are 7 and welcomed here in Chile. They are 8 given food and water by the public. Some people even 9 jackets for the dogs or put out beds for them to sleep in.There are an estimated 2.5 million street dogs in Chile and the canine (犬的) population is 10 . Some people believe that the 11 is getting out of control and that it is 12 to have so many dogs on the streets. The dogs can sometimes cause 13 such as car accidents if they run into the road. Many Chileans think that all the street dogs should be sterilized(使绝育) so that they cannot 14 . Others think that the street dog population should be culled (i.e. reducing the population by killing them).The future of street dogs is 15 , but for now it looks like they are here to stay, with their population expanding year by year.1．A．man B．cat C．dog D．boy 2．A．jumping B．waiting C．hesitating D．refusing 3．A．partners B．owners C．toys D．food 4．A．disappointed B．nervous C．shocked D．angry 5．A．aggressive B．thirsty C．hungry D．sensitive 6．A．lonely B．weak C．friendly D．strong 7．A．controlled B．accepted C．caught D．received 8．A．often B．never C．merely D．barely 9．A．wear B．make C．change D．sell 10．A．aging B．raising C．growing D．declining11．A．policy B．position C．behavior D．situation 12．A．unacceptable B．reasonable C．unusual D．interesting 13．A．diseases B．fears C．problems D．questions 14．A．bite B．breed C．bark D．grow 15．A．bright B．different C．promising D．uncertain二、阅读理解Dorothy and her friends the Scarecrow (稻草人), the Tinman (铁皮人) were walking through the forest with Toto. Suddenly, a great Lion came running at them from the trees. With one blow of his paw, he turned the Scarecrow over and over to the edge of the road, and then he struck at the Tinman with his sharp claws. But, to the Lion’s surprise, he could make no impression on the tin, although the Tinman fell over in the road and lay still. Then little Toto ran up to the Lion and started barking. The Lion was going to hit him too, but Dorothy came between him and the dog, shouting:“Don’t you dare to bite Toto! A big animal like you is going to bite this poor little dog? You are nothing but a coward (胆小鬼)!”The Lion’s face suddenly changed from mad to sad.“I know it,” said the Lion, hanging his head in shame. “I’ve always known it. But how can I help it?” he sighed.“Look at what you did to Scarecrow!” said Dorothy. She picked up the Scarecrow and set him upon his feet, while she put him into shape again.“I’m terribly sorry, Scarecrow,” said the Lion. “You seemed so scary that I had to try and make you run away. Usually, when people and animals see me, they run, but you didn’t.”“Why are you so scared of us?” asked Dorothy. “You’re a lion! Lions are the kings of the forests.”“I can’t help being scared. Whenever there is danger, my heart beats fast.”“Well,” said the Tinman, “maybe you can join us. I have no heart and Scarecrow has no brain. Dorothy and the little dog are dying to go home, very far away. We are going to find the Wizard of Oz for help. Why not come with us and ask him for courage?”“But I am scared to go!” said the Lion.“Everything will be fine,” comforted Dorothy. “There’s nothing to fear when we are alltogether. We’ll all become better.”“Then, if you don’t mind, I’ll go with you,” said the Lion. “As long as I know myself to be a coward, I shall be unhappy!”16．What does the underlined “him” in paragraph 1 refer to?A．The Scarecrow.B．The Tinman.C．The Lion.D．Toto. 17．Which of the following can best describe the Lion in the text?A．Strong but not brave.B．Wild but open-minded.C．Smart but not honest.D．Shy but warm-hearted.18．Why did the Lion try to hit Dorothy and her friends?A．They tried to beat it.B．It was afraid of them.C．They wanted to catch it.D．It was the king of the forest. 19．What do we know about the Tinman?A．He could free the Wizard of Oz.B．He wanted to go home far away.C．He invited the Lion to join them.D．He was a robot with no thoughts. 20．What can we infer about the Lion from the last paragraph?A．It hated to work for long.B．It would live a simple life.C．It minded joining the team.D．It would try to find courage.Rainforests provide much of the world’s oxygen. People have been trying to protect them for years. But another type of forest, the cloud forest, is just as important to humans.These forests are at the tops of mountains, generally near the equator (赤道). These wet, wooded mountaintops are mainly in African and Central and South American countries. They are called “cloud forests” because their height allows for the formation of clouds among the trees. The trees in these forests pull water out of the clouds. The water gathers on the leaves and falls into small rivers below, which flow into towns at the bottom of the mountain. The yearly rainfall in these areas is about 180 centimetres. Cloud forests can pull in up to 60 percent of that. The water is important to the plants and the people in the area. It helps them survive.Cloud forests are also home to countless species of plants that can’t be found anywhere else. One small cloud forest has as many types of plants as there are in all of Europe. In fact, there are so many that scientists haven’t made a complete list of them yet.These forests are being destroyed at an increasing speed. Trees are being cut down, androads are being built in their place. Some people have a goal to get government money to protect the forests. But they have had little success so far. Another way is to take the place of the destroyed plants with new ones. That, too, has been difficult because the plants are so special. There’s plenty of work to be done, but saving the cloud forests is still possible with creative solutions.21．Where can you probably find cloud forests?A．In North America.B．Far from the equator.C．In an African country.D．At the foot of mountains.22．How much rainfall is pulled in by the cloud forests in those areas every year?A．About 60 cm.B．About 108 cm.C．About 180 cm.D．About 300 cm.23．What is the main idea of paragraph 3?A．Europe is short of plant types.B．Scientists are working on a list.C．Cloud forests are getting smaller.D．Cloud forests house many plants.24．What will be discussed in the following part of the text?A．Ways to protect cloud forests.B．Goals of cloud forest protectors.C．Difficulties in planting new trees.D．Successes of getting wide support.25．Where can we probably find the text?A．In a storybook.B．In a travel guide.C．In a chemistry textbook.D．In a geography magazine.Colourful felt (毛毡) flowers have been “planted” at different street corners throughoutGuangzhou by young local sculptor (雕塑家) Luo Shengtian. Starting as a graduation project in April, his efforts have now become a group activity in both China and Europe.Luo said he always wanted to repair the city’s “scars”, such as damaged walls or stone stairs by art. Luo mentioned that these colourful felt plants are like a “beautiful warning” to people as they walk by, reminding them to be aware of these damaged street corners.Within one month, Luo “planted” more than 20 flowers in his community. These flowers attracted more than 300 volunteers to join a WeChat group to spread the repair tasks to other places such as Beijing and Fuzhou. “The meaning of the project is to bring art into people’s everyday lives. Sculptures or other works of fine arts are no longer just an idea in the air,” Luo noted. Following the increase of volunteers, it even spread to European cities such as Venice, and Paris.Luo shared an interesting story in Venice, where one of his fans “planted” a felt flower to see how people would respond to the project. The flower was picked up by someone only a day after it appeared in public, but later three new ones were “planted” by a mysterious person overnight. “I was touched by that. Such an artistic focus on our living environment seems to be shared by global creators,” Luo said.Luo is not the only young creator in the city to focus on creatively renewing people’s everyday experiences. More similar projects have been launched, showing younger generations’ care and social responsibility.26．Why does Luo Shengtian “plant” felt flowers in Guangzhou?A．To protect the flowers.B．To fix broken walls.C．To start a group activity.D．To warn people in streets.A．Hard stones.B．Waste buildings.C．Strange shapes.D．Woundedsurfaces.28．What can we learn from paragraph 3?A．Luo created 300 volunteer groups.B．Luo “planted” 20 flowers in Beijing.C．The project’s influence spread abroad.D．The project made art appear in the air. 29．What is the purpose of the story in Venice in paragraph 4?A．To show the art works’ acceptance in Italy.B．To praise a kind stranger whospread the idea.C．To test if people value their living environment.D．To state the flowers have beenwidely “planted”.30．What’s the best title of this text?A．Felt Flowers Beautify Old Cities B．Luo Shengtian, a Gifted SculptorC．A Beautiful Warning from Flowers D．A Project Famous in European Countries三、其他Gardening has been around for as long as humans have been growing food. Today it is known for its health benefits (益处). Taking part in gardening can reduce our bad feelings andyou don’t like to work out in the gym, gardening is an enjoyable way for you to keep fit.We can include gardening in our life in many ways.Decide which plant to grow. Do you have a favourite flower, fruit, or vegetable?32 . Choose a plant that you want to grow according to how much time you have and how much money and energy you can put into.33 . A community garden is a shared place where people grow plants in a large piece of land together. Search online for a community garden near you. It is a good place to ask questions and learn from experienced gardeners.Grow plants indoors.You don’t have to own land to start gardening. 34 . All you need is just a window or artificial (人造的) lightening source, pots, soil, and any other thing that helps a plant grow.Mistakes happen. Not every plant will grow exactly how you want or expect. Almost everyone will experience problems or failure in growing a plant. Don’t lose heart. 35 .A．Find a community garden.B．Turn to experienced gardeners for help.C．Different plants need different amounts of care.D．Plenty of plants grow well indoors in small pots.E．Even standing near a green plant can help you feel more relaxed.F．Learn from your mistakes, and don’t let them keep you from continuing to garden.四、信息匹配下面的材料A~F介绍的是六个周末活动的好去处。

罗湖外国语新高一入学摸底预测题（90分钟，满分100分）姓名________班级________分数________一、单项选择（共10小题；每小题2分，满分20分）()1.As________matter of fact,_________beauty of__________nature there made an excellent impression on me.A.a;the;不填B.a;the;theC.the;the;不填D.a;不填；the()2.The harder you__________,the better progress you___________.A.will workB.work;have madeC.work;will makeD.will work;make()3._________for his good skill,this doctor has a lot of visitors calling for help all the time.A.KnowingB.To knowC.KnownD.To have known()4.It was a cold winter night,and there wasn’t anyone__________the boy could turn for help in the street.A.thatB.whichC.whomD.what()5.He looked very confident and calm during the test,but_____he was extremely nervous.A.in troubleB.in dangerC.in realityD.in surprise()6.Have you determined___________?A.next to do whatB.what to do nextC.how to do nextD.next how to do()7.They are looking forward to_____________to the lecture by the famous professor. A.send B.be sent C.being sent D.sending()8.It was until last year that he___________.A.left his hometown for a new startB.came to realize the important of learning EnglishC.worked as an English teacher at a middle schoolD.set out to build a new house of his town()9.---Jane wasn’t in when Jack came,was she?---_____,but she returned a few minutes later.A.No,she wasB.No,she wasn’tC.Yes,she wasD.Yes,she wasn’t.()10.He has already gone home.But before he left,he____all the mistakes in his translation.A.had correctedB.has correctedC.correctedD.would correct二、完形填空（共15小题；每小题1分，满分15分）阅读下面短文，按照句子结构的语法性和上下文连贯的要求，从11~25各题所给的A、B、C和D项中选出最佳选项。

2020-2021学年深圳外国语学校高一入学考试物理模拟试卷一、单项选择题（本大题10小题，每小题3分，共30分．在每小题给出的四个选项中只有一个是符合要求的．）1．（3分）下面关于质点的正确说法有（）A．乒乓球运动员在研究乒乓球的运动时可把乒乓球看成质点B．研究沿地面翻滚前进的体操运动员的动作可把运动员看成点C．计算火车通过站台的时间虽然不能忽略火车的大小但仍可把火车看成质点D．小的物体运动可看成质点，大的物体运动就不能看成质点【解答】解：A、乒乓球运动员研究乒乓球在旋转的时候，是不能看成质点的，但研究乒乓球运动的轨迹时，可以把乒乓球可知质点。

故A正确；B、在体操比赛中，评委要看运动员的形体动作的情况，此时人的形状是不能忽略的，所以不能看成质点，故B错误；C、研究一列火车通过站台的时间时，火车的长度相对于站台来说是很大的，此时不能忽略火车的长度，不能看成质点，故C错误；D、能否看成质点，与质量大小无关，质量很小的物体不一定能看成质点，如其大小和形状对所研究的问题影响很大，就不能看成质点，而某些情况下地球也可以看成质点，比如地球的公转，故D错误；故选：A。

2．（3分）下列关于参考系的正确说法有（）A．研究地面上物体的运动，必须选取地面为参考系B．被选为参考系的物体是一定不动的C．质点运动的轨迹是直线还是曲线，与参考系的选取无关D．质点运动的时间，与参考系选取无关【解答】解：A、研究物体的运动时，参考系是可以任意选取的（但不能选研究对象本身为参考系），故A错误；B、自然界中的一切物体都处在永恒的运动中，被选做参考系的物体只是被假定不动，故B错误；C、同一物体的运动，选择不同的参考系所观察到的轨迹可能不同，故C错误；D、质点运动的时间，与参考系选取无关，故D正确。

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广东省深圳市罗湖外国语新2020-2021学年高一上学期入学分班模拟考试英语试题（90 分钟，满分100 分）一、单项选择（共10 小题；每小题2 分，满分20 分）( ) 1. As ________matter of fact, _________ beauty of __________ nature there made an excellent impression on me.A. a; the; 不填B. a; the; theC. the; the; 不填D. a; 不填；the( ) 2. The harder you__________, the better progress you ___________.A. will workB. work; have madeC. work; will makeD. will work; make( ) 3. _________for his good skill, this doctor has a lot of visitors calling for help all the time.A. KnowingB. To knowC. KnownD. To have known( ) 4. It was a cold winter night, and there wasn’t anyone __________the boy could turn for help in the street.A. thatB. whichC. whomD. what( ) 5. He looked very confident and calm during the test, but _____ he was extremely nervous.A. in troubleB. in dangerC. in realityD. in surprise( ) 6. Have you determined ___________?A. next to do whatB. what to do nextC. how to do nextD. next how to do( ) 7. They are looking forward to _____________ to the lecture by the famous professor.A. sendB. be sentC. being sentD. sending( ) 8. It was until last year that he ___________.A. left his hometown for a new startB. came to realize the important of learning EnglishC. worked as an English teacher at a middle schoolD. set out to build a new house of his town( ) 9. ---Jane wasn’t in when Jack came, was she?---_____, but she returned a few minutes later.A. No, she wasB. No, she wasn’tC. Yes, she wasD. Yes, she wasn’t.( ) 10. He has already gone home. But before he left, he____ all the mistakes in his translation.A. had correctedB. has correctedC. correctedD. would correct二、完形填空（共15 小题；每小题1 分，满分15 分）阅读下面短文，按照句子结构的语法性和上下文连贯的要求，从11~25 各题所给的A、B、C 和D项中选出最佳选项。